Question: Solve for $x$ : $2x^2 - 6x - 20 = 0$
Answer: Dividing both sides by $2$ gives: $ x^2 {-3}x {-10} = 0 $ The coefficient on the $x$ term is $-3$ and the constant term is $-10$ , so we need to find two numbers that add up to $-3$ and multiply to $-10$ The two numbers $2$ and $-5$ satisfy both conditions: $ {2} + {-5} = {-3} $ $ {2} \times {-5} = {-10} $ $(x + {2}) (x {-5}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 2) (x -5) = 0$ $x + 2 = 0$ or $x - 5 = 0$ Thus, $x = -2$ and $x = 5$ are the solutions.